bs {splines} | R Documentation

## Generate a Basis for Polynomial Splines

### Description

Generate the B-spline basis matrix for a polynomial spline.

### Usage

    bs(x, df = NULL, knots = NULL, degree = 3, intercept = FALSE,
       Boundary.knots = range(x))

### Arguments

`x` | the predictor variable.
`df` | degrees of freedom; one can specify `df` rather than `knots`; `bs()` then chooses `df-degree-1` knots at suitable quantiles of `x`.
`knots` | the internal breakpoints that define the spline. The default is `NULL`, which results in a basis for ordinary polynomial regression. Typical values are the mean or median for one knot, quantiles for more knots. See also `Boundary.knots`.
`degree` | degree of the piecewise polynomial—default is 3 for cubic splines.
`intercept` | if `TRUE`, an intercept is included in the basis; default is `FALSE`.
`Boundary.knots` | boundary points at which to anchor the B-spline basis (default the range of the data). If both `knots` and `Boundary.knots` are supplied, the basis parameters do not depend on `x`. Data can extend beyond `Boundary.knots`.

### Value

A matrix of dimension `length(x) * df`, where either `df` was supplied or if `knots` were supplied, `df = length(knots) + 3 + intercept`. Attributes are returned that correspond to the arguments to `bs`, and explicitly give the `knots`, `Boundary.knots` etc for use by `predict.bs()`.
`bs()` is based on the function `spline.des()`. It generates a basis matrix for representing the family of piecewise polynomials with the specified interior knots and degree, evaluated at the values of `x`. A primary use is in modeling formulas to directly specify a piecewise polynomial term in a model.

### References

Hastie, T. J. (1992) Generalized additive models. Chapter 7 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.

### See Also

`ns`, `poly`, `smooth.spline`, `predict.bs`, `SafePrediction`

### Examples

    data(women)
    bs(women$height, df = 5)
    summary(fm1 <- lm(weight ~ bs(height, df = 5), data = women))

    ## example of safe prediction
    plot(women, xlab = "Height (in)", ylab = "Weight (lb)")
    ht <- seq(57, 73, len = 200)
    lines(ht, predict(fm1, data.frame(height=ht)))

    ## Consistency:
    x <- c(1:3,5:6)
    stopifnot(identical(bs(x), bs(x, df = 3)),
              !is.null(kk <- attr(bs(x), "knots")),# not true till 1.5.1
              length(kk) == 0)

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